{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "64448bd9-7802-43aa-b8cd-8265dc474c24",
   "metadata": {},
   "source": [
    "# Trapped Ion Qubits\n",
    "\n",
    "These examples all cover dynamical simulation of trapped ion qubits. These examples use small systems, but note that the GPU will only provide an advantage for systems with total dimension of O(1000). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4fd221c-e31e-4082-b2ca-3b9418d050ca",
   "metadata": {},
   "source": [
    "## GHZ state\n",
    "This example shows how to prepare a GHZ (`Greenberger-Horne-Zeilinger`) state using trapped ions and CUDA-Q. We'll use the effective spin model from the famous `Sørensen-Mølmer` [paper.](https://www.quantumoptics.at/images/publications/dissertation/ThesisMvM_Web.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bdf1a7fc-95a6-4814-84c0-f9c83a8d5ed8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running time evolution...\n",
      "\n",
      "Results at GHZ time (χt = 0.393):\n",
      "P(|gggggggg⟩) = 0.500\n",
      "P(|eeeeeeee⟩) = 0.500\n",
      "Total in extremes: 0.999\n",
      "GHZ state quality: 1.000 (1.0 = perfect)\n",
      "Perfect GHZ would have P(gg) = P(ee) = 0.5\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "What we're doing:\n",
    "- Start with N ions all in ground state `|gg...g⟩`\n",
    "- Apply an effective Hamiltonian H = 4χJ_x²  \n",
    "- Watch the system evolve into a GHZ superposition: `(|gg...g⟩ + |ee...e⟩)/√2`\n",
    "\n",
    "This tutorial uses the simplified effective model (`Eq. 2` from the paper).\n",
    "\"\"\"\n",
    "\n",
    "import cudaq\n",
    "from cudaq import spin, Schedule, RungeKuttaIntegrator\n",
    "import numpy as np\n",
    "import cupy as cp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "cudaq.set_target(\"dynamics\")\n",
    "\n",
    "# Physical parameters, these come from the `Sørensen-Mølmer` paper\n",
    "nu = 1.0  # Trap frequency (our reference)\n",
    "delta = 0.9 * nu  # Laser detuning\n",
    "Omega = 0.1 * nu  # Laser strength\n",
    "eta = 0.1  # How strongly lasers couple to motion\n",
    "\n",
    "# The effective coupling strength (this is the key parameter!)\n",
    "chi = (eta**2 * Omega**2 * nu) / (2 * (nu**2 - delta**2))\n",
    "\n",
    "N = 8  # Number of ions (start small!)\n",
    "evolution_time = 1.0 / chi  # How long to evolve\n",
    "num_steps = 100  # Time resolution\n",
    "\n",
    "dimensions = {i: 2 for i in range(N)}  # Each ion is a 2-level system\n",
    "\n",
    "# collective spin operator J_x\n",
    "J_x = spin.empty()\n",
    "for i in range(N):\n",
    "    J_x += spin.x(i)\n",
    "J_x /= 2  # Normalize\n",
    "\n",
    "hamiltonian = 4 * chi * J_x * J_x\n",
    "\n",
    "# Set up initial state and time evolution\n",
    "# Start with all ions in ground state `|gg...g⟩`\n",
    "initial_state_vector = cp.zeros(2**N, dtype=cp.complex128)\n",
    "initial_state_vector[0] = 1.0  # |00...0⟩ = `|gg...g⟩`\n",
    "initial_state = cudaq.State.from_data(initial_state_vector)\n",
    "\n",
    "# Set up time points for evolution\n",
    "times = np.linspace(0, evolution_time, num_steps)\n",
    "chi_times = chi * times  # Dimensionless time χt\n",
    "schedule = Schedule(times, [\"t\"])\n",
    "\n",
    "# Create observables to track the populations\n",
    "# We want to measure the probability of being in `|gg...g⟩` and `|ee...e⟩`\n",
    "\n",
    "# Projector onto `|gg...g⟩ = |00...0⟩`\n",
    "P_ground = spin.empty()\n",
    "for i in range(N):\n",
    "    if i == 0:\n",
    "        P_ground = (spin.identity(i) - spin.z(i)) / 2  # `|0⟩⟨0|`\n",
    "    else:\n",
    "        P_ground = P_ground * (spin.identity(i) - spin.z(i)) / 2\n",
    "\n",
    "# Projector onto `|ee...e⟩ = |11...1⟩`\n",
    "P_excited = spin.empty()\n",
    "for i in range(N):\n",
    "    if i == 0:\n",
    "        P_excited = (spin.identity(i) + spin.z(i)) / 2  # `|1⟩⟨1|`\n",
    "    else:\n",
    "        P_excited = P_excited * (spin.identity(i) + spin.z(i)) / 2\n",
    "\n",
    "observables = [P_ground, P_excited]\n",
    "\n",
    "# Run the simulation!\n",
    "print(\"Running time evolution...\")\n",
    "evolution_result = cudaq.evolve(\n",
    "    hamiltonian,\n",
    "    dimensions,\n",
    "    schedule,\n",
    "    initial_state,\n",
    "    observables=observables,\n",
    "    collapse_operators=[],  # No decoherence for this tutorial\n",
    "    store_intermediate_results=cudaq.IntermediateResultSave.EXPECTATION_VALUE,  # Save expectation values\n",
    "    integrator=RungeKuttaIntegrator())\n",
    "\n",
    "# Extract the results\n",
    "exp_vals = evolution_result.expectation_values()\n",
    "pop_ground = [exp_vals[i][0].expectation() for i in range(len(times))]\n",
    "pop_excited = [exp_vals[i][1].expectation() for i in range(len(times))]\n",
    "\n",
    "# The GHZ state appears at a special time: χt = π/8\n",
    "ghz_chi_t = np.pi / 8\n",
    "ghz_time_idx = np.argmin(np.abs(chi_times - ghz_chi_t))\n",
    "ghz_pop_ground = pop_ground[ghz_time_idx]\n",
    "ghz_pop_excited = pop_excited[ghz_time_idx]\n",
    "\n",
    "print(f\"\\nResults at GHZ time (χt = {ghz_chi_t:.3f}):\")\n",
    "print(f\"P(|{'g'*N}⟩) = {ghz_pop_ground:.3f}\")\n",
    "print(f\"P(|{'e'*N}⟩) = {ghz_pop_excited:.3f}\")\n",
    "print(f\"Total in extremes: {ghz_pop_ground + ghz_pop_excited:.3f}\")\n",
    "\n",
    "# Check GHZ state quality\n",
    "# For perfect GHZ state: `P(gg) = P(ee) = 0.5`\n",
    "ghz_quality = 1 - 2 * abs(\n",
    "    ghz_pop_ground - 0.5)  # Distance from ideal probability\n",
    "print(f\"GHZ state quality: {ghz_quality:.3f} (1.0 = perfect)\")\n",
    "print(f\"Perfect GHZ would have P(gg) = P(ee) = 0.5\")\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(chi_times,\n",
    "         pop_ground,\n",
    "         'b-',\n",
    "         linewidth=2,\n",
    "         label=f\"|{'g'*N}⟩ (all ground)\")\n",
    "plt.plot(chi_times,\n",
    "         pop_excited,\n",
    "         'r-',\n",
    "         linewidth=2,\n",
    "         label=f\"|{'e'*N}⟩ (all excited)\")\n",
    "plt.axvline(ghz_chi_t,\n",
    "            color='gray',\n",
    "            linestyle='--',\n",
    "            alpha=0.7,\n",
    "            label=\"GHZ time\")\n",
    "plt.axhline(0.5, color='black', linestyle=':', alpha=0.5, label=\"Perfect GHZ\")\n",
    "\n",
    "plt.xlabel(\"Dimensionless time (χt)\")\n",
    "plt.ylabel(\"Population\")\n",
    "plt.title(f\"Evolution to GHZ State ({N} trapped ions)\")\n",
    "plt.legend()\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 1)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
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